solar radiation definitions incident solar...

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Solar energy

solar radiation definitions incident solar energy

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Sun

closest star centre of our planetary system – solar system

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Sun

diameter 1 392 000 km 109 x larger than Earth weight 2 x 1030 kg 330 000 x greater than Earth

99,86 % weight of solar system consists of: 70 % hydrogen H, 28 % helium He, 2 % other elements

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Sun

origin of solar energy in nuclear reactions

nuclear fusion takes place inside the Sunat high temperatures 106 K and pressures 1010 MPasynthesis of hydrogen nuclei (H) → helium nuclei (He)

564 x 109 kg/s H transforms to 560 x 109 kg/s He mass difference 4 x 109 kg/s is radiated in the form of energy

E = m.c2

radiative power: 3,6 x 1026 W

specific radiated power (density): 6 x 107 W/m2

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Sun

core (to 23 % radius)temperature 106 K, X-ray radiation90 % of Sun’s energy generated

radiative zone (from 23 to 70 % radius)temperature falls down to 130 000 Kradiative energy transfer (fotons)

convective zone (from 70 to 100 % radius)lower density, convective energy transfer

photosphere (visible surface of Sun)temperature 5800 K, solar radiation

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Spectral density of radiative flux

Sun radiates as perfect black body with surface temperature 5800 K

spectral density of radiative solar flux (Planck’s law)1

5

212),(

Tk

ch

č echTE

[W/m2.m]

h = 6,6256 x 10-34 J.s Planck’s constantk = 1,3805 x 10-23 J/K Boltzmann’s constantc = 2,9979 x 108 m/s light velocity in vacuumT thermodynamic surface temperature [K]

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Planck’s law

Černý, M. (2008)wavelength

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Spectral density of radiative fluxVISUV NIR

UV: ultraviolet radiation 0,2 až 0,4 m

UVA (> 0,32 m), UVB, UVC (< 0,28 m)

VIS: visible radiation 0,40 to 0,75 m

NIR: near infrared radiation 0,75 až 5 m

black body 5800 K

wavelength [nm]

dens

ity of

radia

tivef

lux [W

/(m2 .n

m)]

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black body 5800 K

Solar energy irradiated

50 %41 %9 %

VISUV NIR

wavelength [nm]

dens

ity of

radia

tivef

lux [W

/(m2 .n

m)]

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Wien’s law

maximum of radiative flux – seeking the extreme of Planck’s function

28980),(max

TTEč

[m.K] Wien’s law

5800 K: max = 0,5 m

373 K: max = 7,8 m

black body 5800 K

wavelength [nm]

dens

ity of

radia

tivef

lux [W

/(m2 .n

m)]

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Propagation of solar energy

power spreads to larger area with increasing distance from Sun 0,5 x 10-9 of the irradiated Sun’s power is incident on Earth

radiative flux 1,7 x 1017 W solar „beams“ considered as parallel (32’)

Sun Earth

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Earth rotates around Sun

Sun

Earth

eliptic orbit (almost circular), Sun in one of focusses

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Radiative flux density out of atmosphere

solar radiative flux incident on area unit perpendicular to direction ofpropagation

changes during the year, variable distance Sun-Earth (eliptic orbit)change of distance 1,7 %, change of flux 3,3 %

value for mean distance Sun-Earth

solar constant Gsc = 1367 W/m2 (value from WRC, 1 %)

original measurements Ch. Abbot in mountains 1322 W/m2, todaysatellites

Merkur: 9040 W/m2 ... Neptun: 1,5 W/m2

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Radiative flux density out of atmosphere

1320

1340

1360

1380

1400

1420

0 50 100 150 200 250 300 350dny v roce

Gon

[W/m

2 ]

365

360cos033,01 nGG scon

day in the year

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Solar radiation passing the atmosphere

solar radiation enters the atmosphere (no definite boundary, exosphere continuosly fading to interplanetary space)

ionosphere (60 km)atmospheric gases O2, N2 absorb ultraviolet a x-ray radiation, becoming ionised

ozonosphere (20 až 30 km)ozon O3 absorbs rest of harmfull ultraviolet radiation (UVC)

troposphere (lowest layer, clouds)water vapor, CO2, dust, water droplets absorb infrared radiation

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wavelength [nm]

dens

ity of

radia

tivef

lux [W

/(m2 .n

m)]

AM0: spectrum outside atm.

AM1: perpendicular pass

AM1,5: spektrum at 48°

AM2: spektrum at 60°

solar radiation: 0,3 to 3 m

outside atmosphere

sea level

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Annual balance

reflection from atmosphere 34 % absorption in atmosphere 19 % incident and absorbed by Earth surface 47 %

absorbed at surface

emitted back 14 % energy of environment

evaporation (oceans) 23 % water energy

convection, winds 10 % wind energy

biologic reactions, photosynthesis 1 ‰ energy of biomass

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Solar geometry

surface slope surface azimuth latitude

time, date time angel declination Sun height h Sun azimuth s

incidence angle

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Surface position

latitude convention: north (+), south (-)angle between plane of equator and a line connecting Earth centre and given place on Earth surface

51°

50°

49°

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Surface position

high difference between north andsouth in one country

Norway: 57 to 71°

Sweden: 55 to 68°

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Surface orientation

slope angle convention: horizontal 0°, vertical 90°angle between horizontal plane and surface plane

surface azimuth convention: east (-), west (+), south (0°)angle between projection of surface normal and local meridian (south)

J projection

normal

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Declination

21. june

22. december 23. september

21. march

-23.45°

+23.45°

0°

0°

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Declination

tilt angle of Earth’s axis due to precession movement during rotation angle between the line (connecting centres of Earth and Sun) and

equator plane latitude of place on Earth where in given day in the noon the Sun is in

zenith

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Calculation of declination

from calender date DD.MM.

from order of the day in the year n

1097,2998,0sin45,23 MMDD

365

284360sin45,23 n

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Calculation of declination

-30

-20

-10

0

10

20

30

0 50 100 150 200 250 300 350pořadí dne v roce

dekli

nace

[°]

equinoxsolstice

solstice

-23,45°

+23,45°

0° 0°

order of the day in a year

decli

natio

n [°]

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time (hour) angle

angle of virtual translation of Sun above local meridians due to Earthrotation, related to solar noon

Earth is rotating around its axis (360°) once for 24 hours→ translation of Sun by 15° over 1 hour

time angle is calculated from solar time ST

convention: before noon (-), after noon (+)

1215 ST

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Solar time ST

each timezone has a time related to local meridiantimezones of 1 h ~ meridians of 15°

CET: local solar time at meridian 15° east longitude

solar time: daily time defined from virtual translation of Sun

observer at reference meridian: local time = solar time observer out of reference meridian: local time solar time

shift up to 30 minnutes

example: solar noon Prague 14,4° 12:02Brno 16,6 ° 11:53Košice 21,2° 11:35

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Sun altitude h

angle between line connecting surface-Sun and horizontal

complement angle to 90°: zenith angle z

coscoscossinsinsin h

hz 90

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Air mass

ratio between mass of atmosphere passed by solar radiation to mass, which would be passed if Sun is in zenith

AM = 0 outside atmosphere

AM = 1 zenith h = 90°

AM = 1,5 z = 48° h = 42°

AM = 2 z = 60° h = 30°

hAM

z sin1

cos1

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Change of spectrum with air mass

h = 90° AM = 1,00h = 70° AM = 1,06h = 50° AM = 1,31h = 30° AM = 2,00h = 10° AM = 5,76

dens

ity of

radia

tivef

lux [W

/(m2 .n

m)]

wavelength [nm]

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Time of sunrise and sunset

sunrise / sunset: altitude angle = 0°

0coscoscossinsinsin h

tgtg arccos2,1

time angle of sunrise / sunset

theoretical period of sunshine = time between sunrise and sunset

15

2 2,1 t

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Azimuth of Sun s

angle between projection of line connecting surface-Sun and localmeridian (south)

convention: measured from southeast (-), west (+)

sincoscossin

hs

Sun

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Altitude and azimuth of Sun

source: solarpraxis

22. december

23. september21. march

21. june

J

S

V

Z

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Incidence angle

angle between line connecting surface-Sun and surface normal

shh cossincoscossincos

Sun

surfacenormal

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Solar radiation - definitions

solar irradiance G [W/m2] - radiative power incident at area unit, density of solar radiative flux

solar irradiation H [kWh/m2, J/m2] – density of radiative energy, integral of flux density per time period, e.g. hour, day, ...

2

1

.

dGH

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direct solar radiation (index „b“, beam) – withoutscattering in atmosphereangle dependent, significant intensity in one direction

diffuse solar radiation (index „d“, diffuse) – scattered in atmosphereall-directions, isotropic: identical intesity in all direction

reflected solar radiation (index „r“, reflected) – reflectionfrom terrain, buildingsusual surfaces reflect diffusively – considered togetherwith diffuse radiation

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source: solarpraxis

reflection from air molecules, dustparticles, ice crystals

reflection fromterrain

reflectedradiation

directradiation

diffuse radiation

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direct normal solar irradiance (on surface perpendicular to directionof propagation) after passing atmosphere

ZGG onbn exp

Gon normal solar irradiance above atmosphereZ attenuation factor

91018,0)101(0015,2

)sin003,0(sin38076,94

5,02

vL

hh

h Sun altitudeLv elevation above sea-level [m]

[W/m2]

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Attenuation factor

how many times the clear atmosphere should be „heavier“, to havethe same transmissivity as the real polluted atmosphere

polluted means also water vapor not only dust, emissions, etc.

gives attenuation of solar flux when passing the real atmosphere

00

0

lnlnlnln

bn

bnn

GGGGZ

Gb0 direct irradiance after passing completely clearatmosphere (with Z = 1)

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Attenuation factor

5,03,752,751,9annualaverage

4,23,12,21,5XII.4,53,32,31,6XI.4,93,62,61,8X.5,34,02,92,1IX.5,74,33,32,3VIII.5,84,43,52,3VII.5,74,33,42,3VI.5,54,23,22,0V.5,34,02,91,9IV.4,73,52,51,8III.4,33,22,21,6II.4,13,12,11,5I.

industrialcitiescontrysidemountains

Average monthly values for Zfor locations with different environment

Monthsimplified:

mountains Z = 2

countryside Z = 3

cities Z = 4

industrial Z > 5

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Solar irradiance on general surface

total solar irradiance on generally sloped and oriented surface

rTdTbTT GGGG

directirradiance

diffuseirradiancefrom sky

diffusereflectedirradiance

diffusecharacter

[W/m2]

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Solar irradiance on general surface

direct solar irradiance on given surface

sky diffuse solar irradiance on given surface

reflected diffuse solar irradiance on given surface

zbbbnbT G

hGGG

coscos

sincoscos

ddT GG

2

cos1

dbgrT GGG

2cos1

[W/m2]

[W/m2]

[W/m2]

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Terrain reflectance (albedo)

ratio between reflected and incident solar irradiance

for calculations considered g = 0,2

usual surfaces 0,10 až 0,15

snow 0,90

Earth albedo (planet) 0,30 (average)

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Solar irradiance on horizontal plane

direct solar irradiance on horizontal plane

diffuse solar irradiance on horizontal plane

simplified model: 1/3 of solar radiatin „lost“ in atmosphere comes to horizontal plane (sin h) as a diffuse isotropic radiation

hGG bnb sin

hGGG bnond sin33,0

[W/m2]

[W/m2]

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Solar irradiation on general surface

theoretical daily solar irradiation, integration of irradiance on a plane from sunrise 1 to sunset 2

2

1

,,

dGH TthdayT

mean daily solarirradiance

t

thdayTmT

HG

,,

,

[kWh/(m2.day)]

[W/m2] HT,day,th

t

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Influence of slope

optimum slope: summer 20-30° winter 75-90° annual 35-45°

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12měsíc

HT,

den,

teor [

kWh/

m2 .den

]

0° 30° 45° 75° 90°

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12měsíc

HT,

den,

teor [

kWh/

m2 .den

]

0° 30° 45° 75° 90°

azimuth 0° (south) azimuth 45° (SW, SE)

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Solar irradiation of general surface

diffuse daily solar irradiation, integration of diffuse solar irradiance on a plane from sunrise 1 to sunset 2

2

1

,,

dGH dTdifdayT

HT,day,th

HT,day.dif

GT,m

tabelled in literature for given:slopes, azimuths, locations (attenuation factors)}

[kWh/(m2.day)]

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Real duration of sunshine

duration of direct solar radiation > 120 W/m2

i

iss ,

relative period of sunshine

t

sr

[h]

[-]

meteo-institute (CZ) presents the values for 22 locations

120 W/m2

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Real duration of sunshine

1 8101 8261 6911 899

30423635XII.

56485553XI.

116115108117X.

179188174190IX.

230233219238VIII.

270252238266VII.

258249226266VI.

232241207247V.

163185164187IV.

142149136157III.

88778290II.

46474653I.

BrnoHradec KrálovéČeské BudějovicePraha

Real duration of suhshine s [h]Month

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Real duration of sunshine in CZ

1400 – 1900 h/year

source: ČHMÚ

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Real duration of sunshine in Europe

> 2500 h

< 1200 h

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Total irradiation on given plane

daily solar irradiation

monthly solar irradiation

difdayTrthdayTrdayT HHH ,,,,, 1

dayTmonT HnH ,,

annual solar irradiation

XII

ImonTyearT HH ,,

[kWh/(m2.day)]

[kWh/(m2.mon)]

[kWh/(m2.year)]

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Annual solar irradiation in CZ

slope 30 až 45°, south orientation: 1000 až 1200 kWh/m2

slope 90°, south orientation: 750 až 900 kWh/m2

source: ČHMÚ

MJ/m2

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Optimum slope for Central Europe ?

southeast west

southeast - southwest

15-6

0°

slope

azimuth

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Solar energy: typical values

solar irradiance G (power)

clear sky 800 to 1000 W/m2

semibright 400 to 700 W/m2

overcast 100 to 300 W/m2

solar irradiation H (energy)

winter 3 kWh/(m2.day)

spring, autumn 5 kWh/(m2.day)

summer 8 kWh/(m2.day)

solar radiation definitions incident solar...

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